The `Eed Prayer is waajib (obligatory) according to the majority of
scholars. The Prophet performed it consistently and commanded all the
people to go out for it.
He even specifically commanded all of the women to attend; Umm `Atiyyah () narrated that the Prophet commanded:

Let the free women, the virgins, and the menstruating women go out to
attend the `Eed prayer, and witness the good and the supplications of the
believers. As for the menstruating women, they should stay away from the
musallaa. (i.e., should not participate in the prayer itself).1

Shaykh ul-Islaam Ibn Taymiyyah (r) said:

"... Thus we lean towards the opinion that Salaat ul-`Eed is fard `Ayn
(individual obligation) on each individual. This is the opinion of Abu
Haneefah2 and others, and is one of the two reported opinions of
ash-Shaafi`ee and of the school of Ahmad.
The opinion held by some people, that it is not waajib, it is extremely
unlikely, because it is one of the greatest rites of Islam; more people
gather for it than for Friday; and the Takbeer has been legislated for its
sake. The opinion of those who say that it is far kifaayah (communal
obligation) is unjustified ..."3

Ash-Shawkaanee (r) said:

"Note that the Prophet consistently performed this prayer on every
`Eed, never neglecting it. He commanded the people to go out for it; he
even commanded the free women, the virgins, and the menstruating women to
go out, instructing the latter to refrain from praying, in order for all
of them to witness this good and the Muslims' supplications. He
further commanded the woman who did not own a jilbaab (outer overall
garment for women) to borrow her friend's.4
All of this proves that this prayer is waajib on every individual, not only
a kifayah obligation. Commanding the people to go out for it entails the
command to perform the prayer (for those who have no excuse). This is the
content of his address, because going out is a means for performing
the prayer (an end); if the means is obligatory, then the end is. And this
obligation applies to men even more so that women.
A further evidence is that it overrides the Friday prayer when both occur
on the same day5. That which is not waajib cannot override that which is.
Furthermore, it is confirmed that the Prophet performed it
consistently in Jamaa`ah (congregation) from the time that it was
legislated until he died. To this is added his command to people to go out
for it."6

"The Prophet's command mentioned here indicates obligation; when it
is waajib to go out for it, it is waajib to pray it, because of its higher
priority. Thus the truth is that it is an obligation - not a mere
recommendation."7

Abu Hurayrah (t) narrated that one time the `Eed fell on a Friday. The Messenger of Allaah said: Two `Eeds have come together on this day of yours; so whoever wishes, he is excused from the Jumu`ah (Friday) prayer. But as for us, we shall gather for the Jumu`ah. [Abu Daawood and Ibn Maajah with a hasan chain of narrators]
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As-Sayl ul-Jarraar 1:315. See also Nayl ul-awtaar and ar-Rawat un-Nadiyyah.
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